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Active Bragg angle compensation is demonstrated for shaping ultrafast, mid-infrared pulses. The effects of angular dispersion introduced by the acousto-optic modulator on the temporal characteristics of the pulse are measured by autocorrelating the output from the pulse shaper. The time duration of the output pulses were measured to be thirty times shorter than pulses produced with a constant frequency amplitude waveform. This approach acts to mitigate angular dispersion in Bragg-regime acousto-optic devices, thus affording the ability to shape ultrafast pulses of light with broad bandwidths that are centered at mid-IR wavelengths and longer.
©2012 Optical Society of America
1. Introduction
Multidimensional optical spectroscopies have proven to be measurements of high utility for investigations regarding a variety of physical and chemical phenomena. For example, two- and three-dimensional electronic spectroscopies have been employed to measure charge transfer processes and structural rearrangements in proteins related to these processes [1–3]. Two- and three-dimensional infrared spectroscopy has gained broader use in examining structural rearrangements and solvent dynamics involved in charge transfer [4, 5], charge transfer in organic photovoltaic materials [6], nucleic acids [7, 8], and protein folding events [9–11]. In fact, the multitude of chemical systems investigated using multidimensional nonlinear spectroscopies only continues to grow at a rapid pace. Recent advances in pulse shaping have opened up new possibilities for multidimensional electronic and multidimensional infrared spectroscopies due to the simplicity of beam geometries made available, higher signal-to-noise ratios obtained, and higher spectral acquisition rates [9, 12–14]. In addition, advancements in the use of broadband light sources have also been made. For example, non-linear optical spectroscopy experiments are now being performed with continuum mid-IR ultrafast light sources [15–18]. Direct pulse shaping in the mid-IR and continuum mid-IR ultrafast light sources are two technologies with promise of pushing the field of multidimensional IR spectroscopy forward. However, these two technologies are not necessarily compatible with each other due to the geometrical constraints associated with pulse shaping.
In modulating an optical pulse by pulse shaping, the temporal profile of a pulse is determined by the bandwidth of the pulse and the relative phases between each wavelength. By manipulating each frequency independently, it is possible to produce arbitrarily modified pulses. This process is represented as E’(ω) = M(ω)E(ω), where E(ω) is the original optical field represented in the frequency domain, M(ω) is the mask that represents the modification to the pulse, and E’(ω) is the resulting optical field. For example, a mask that produces a double pulse is given by
where τ is the separation between the pulses, and φ1 and φ2 are the absolute phases of each pulse in the pulse pair. This waveform is utilized in 2D IR spectroscopy and 2D electronic spectroscopy experiments [19–21].Pulse shapers developed recently for directly shaping mid-IR light are based on acousto-optic modulators (AOM) that operate in the Bragg regime. As such, it is the geometry of the acousto-optic interaction that controls the efficiency of the modulation of the optical wave and the efficiency of the diffraction of the light. Achieving operation in the Bragg regime requires the interaction length between light and sound to be long. In this case, phase-matching conditions are important. Momentum conservation between the light and sound waves requires that the incident and diffracted optical waves both be at the Bragg angle relative to the acoustic wave for efficient diffraction [22–24]. If this condition is not satisfied, a wavevector mismatch results which gives rise to angular dispersion. As pulse shapers are employed with longer wavelength light or larger optical bandwidth systems, angular dispersion increases due to the larger differences in Bragg angle from one side of the spectrum of the pulse to the other.
For the majority of AOM-based pulse shapers, a sine wave is used to drive the AOM device. The shaping mask is integrated into the sine wave by separating the waveform into amplitude and phase portions, and implementing the masks as amplitude and phase modifications to the sine wave as follows:
where fc is the center frequency of the AOM and Mamp(t) and Mφ(t) are the time dependent amplitude and phase portions of the shaping mask.The pulse shapers utilized for shaping mid-IR light are comprised of a Germanium acousto-optic modulator (Ge-AOM) fixed in the Fourier plane of a zero-dispersion compressor (ZDC) line. The frequency components in the mid-IR pulse are spatially resolved in the first half of the zero-dispersion compressor and directed onto the Ge-AOM, often by a gold folding mirror. In the case of a constant frequency and amplitude acoustic wave being driven across the crystal, only one specific frequency component impinges on the AOM at the proper Bragg angle. The Bragg angle is given by,
where λ is the optical wavelength, f is the center acoustic frequency, ν is the acoustic velocity in the medium, and n(λ) is the wavelength dependent index of refraction of light. This equation gives a single Bragg angle for a specific wavelength and acoustic frequency. Thus, only one optical frequency component will diffract off the acoustic wave front at the Bragg angle, while all of the other components will deviate from the Bragg angle resulting in angular dispersion of the light. Figure 1A , depicts this result. Each frequency component is incident on the AOM at a constant angle, θB, which is the Bragg angle for the center frequency component. The other frequency components will diffract at angles governed by the phase-matching direction given by the addition of the optical wavevector and the acoustic wavevector. In order to mitigate angular dispersion introduced by the AOM, the acoustic wave must have the proper frequency at specific positions in the AOM crystal such that the Bragg condition is satisfied for all frequency components contained in the mid-IR pulse. Figure 1B depicts the case of the acoustic wave front arriving at the appropriate part of the crystal in order for all optical frequencies to be incident and diffract at the Bragg angle, θB.
Fig. 1 Illustrations of Bragg deflections in an AOM crystal for spatially separated frequencies of light using a constant frequency acoustic wave (A) and a Bragg angle compensated acoustic wave (B). The solid and dashed lines in the AOM crystal represent the acoustic wave. The different frequencies of light, each represented by different colors, all enter the device at the same angle, θB.
In order to realize the situation depicted in Fig. 1B, we have developed a waveform to actively satisfy the Bragg condition. This is accomplished by utilizing the arbitrary waveform generator (AWG) to take advantage of the full acoustic bandwidth available and generating an acoustic wave with a frequency that is dependent upon the optical wavelength of the pulse. The AOM has an acoustic velocity that is constant and because a pair of folding mirrors are used to direct all optical frequencies to and from the AOM, a constant, C, can be defined,
where λo is the center wavelength of the pulse and fc is the center frequency of the acoustic wave. Using the Bragg angle equation, a new acoustic frequency is calculated that depends on the wavelength of light being diffracted, Substituting this expression into the equation for a pulse modulating waveform gives,where the shaping mask is described by its time dependent amplitude Mamp(t), and time dependent phase, Mφ(t). Although the wavelength dependent acoustic frequency is included, this equation is not correct since it is only true for constant frequencies. Instead, the instantaneous phase must be considered, using the equation,where ϕ(t) is the instantaneous phase expressed aswhere ϕo is the initial phase. Equation (9) requires the function for frequency to be in terms of time with respect to the acoustic wave while Eq. (6) gives the frequency in terms of wavelength. Using the same calibration procedures required to map the IR frequency onto the spatial dimension of the mask, as well as the time-dependence of the RF mask produced by the AWG, the Bragg angle correction frequency can be obtained in terms of the acoustic waveform time scale. This gives a new waveform equation,where fλ(τ) is the Bragg angle compensated acoustic frequency converted to the time scale of the acoustic wave. Below we describe the experimental implementation of this waveform, provide the temporal pulse characteristics produced utilizing this waveform, and demonstrate its utility in 2D IR spectroscopy.2. Experimental methods
The design and layout of our two-dimensional infrared spectrometer utilizes a partially collinear beam geometry, such as those implemented in pump-probe experiments; an acousto-optic modular is placed in the pump beam-line similar to work demonstrated by Zanni and associates. Briefly, our spectrometer consists of an ultrafast pulsed, light source, a pulse shaper, and multi-element detection system. A Ti:sapphire oscillator (KM Laboratories) produces an 80 MHz pulse train of sub-50 fs, 2.5 nJ pulses centered at 800 nm. The pulses from the oscillator are used to seed a regenerative chirped pulse amplifier (KM Laboratories Wyvern 1000) producing pulses at a 1 kHz repetition rate that are 3 mJ in energy, centered at 800 nm, and are sub-50 fs in duration. These pulses pump an optical parametric amplifier (OPA, Light Conversion TOPAS-C) fit with a difference frequency generation stage, to produce tunable mid-IR light. In this work, the mid-IR pulses are centered at 4830 nm, are 15 µJ in energy, and 100 fs in duration. A long-wave pass filter is used to separate the mid-IR light from any remaining signal and idler light.
The mid-IR pulses are directed into the spectrometer box, and overlapped with a HeNe laser to facilitate alignment. The mid-IR is split into two beam paths using a wedged ZnSe 90:10 (T:R) beam splitter. The majority of the light is directed towards the pulse shaper and the remainder of the light is directed along a second path and serves as the probe beam in our experiments. A Ge-AOM based pulse shaper is used to generate pulse pairs for 2D IR spectroscopy and is described below. A pump-probe beam geometry is used for 2D IR experiments; the pump and probe beams are reflected off of a gold coated 90° off-axis parabolic mirror (152.4 mm f.l.). After the sample the pump and probe beams are collected on an identical parabolic reflector, and are directed towards a spectrometer composed of a Triax 190 spectrometer (Horiba) coupled with a 2x32 element HgCdT (MCT) array detector (Infrared Systems Development and Infrared Associates). The probe beam is directed into the spectrometer and focused onto the entrance slits of the spectrometer using a 100 mm focal length lens. We determine the resolution of the spectrometer by scanning the spectrum of a pulse across one element in the center of the MCT array and compare the width of the water vapor absorption lines to the linear IR spectrum of water vapor in the 5-6 μm region. Based on these data, the resolution of our spectrometer is approximately 4 cm−1 with the chosen grating.
The mid-IR pulse shaper is composed of a Ge-AOM (Isomet Corporation LS600-1109) placed in the Fourier plane of a zero-dispersion compressor line. The geometry utilized is a reflective implementation introduced by Shim, et al. for pulse shaping directly in the mid-IR [25, 26]. The input mid-IR beam is passed over a cylindrical mirror and dispersed by a grating with a blaze wavelength of 5.2 µm and a groove density of 100 ln/mm. The grating is adjusted to a quasi-Littrow configuration, where the diffracted IR light is reflected back on itself, but is tilted downward, and the diffracted beam is collected by a cylindrical mirror (129.4 mm f.l.). The spatially separated and collimated frequency components of the mid-IR beams are reflected off a 3-inch gold folding mirror into the Ge-AOM at the Bragg angle. The second half of the shaper is set up to mirror the first half with identical optics.
As a result of the Ge-AOM being a traveling wave device, the timing between the acoustic waveform and the mid-IR pulse must be synchronized. The oscillator contains a fast photodiode for detecting the 80MHz output pulse train. In order to accommodate the timing of the Ge-AOM, the 80MHz pulse train is diverted into a phase lock loop circuit (Maxim MAX3639). This circuit produces two output signals: a 300 MHz signal used to sync the clock of the AWG to the oscillator and another 80 MHz signal to be reduced to 1 kHz for the regenerative amplifier. In addition the 1kHz signal used to trigger the regenerative amplifier components is sent through a digital delay generator (DDG, Berkley Nucleonics Corp. Model 575). The DDG uses the 1 kHz signal to produce 4 additional 1 kHz signals with independent time delays. The first channel produces a pulse that is delayed by 50 µs that is used to trigger the regen amplifier’s pump laser and Pockels cell. The second channel is used to trigger data acquisition with a delay of 53 µs. Channels three and four are used to trigger the RF amplifier for the Ge-AOM and the AWG (GaGe CompuGen 4302) with delays of 8 µs and 38 µs respectively. This ensures that the acoustic waveform has reached the proper location in the Ge-AOM crystal when the light arrives at the crystal to produce the desired modified pulse. Following the procedure outlined by Middleton et al., a frequency comb is used to correlate the time for the acoustic wave to travel to a spot in the crystal and affect a specific frequency of light [27].
In order to characterize the pulse durations of the shaped pulses, a home-built, non-collinear, intensity autocorrelator is used. In the autocorrelator, the pulse to be measured is split into two equal beams using a D-shaped gold mirror; thus producing the fixed and delay arms typically present in autcorrelators. The beams from each arm are horizontally overlapped with the delay arm at a 90° gold off-axis parabolic mirror (101.6 mm f.l.). Both beams are reflected and focused into a Type I AgGaS2 crystal for frequency doubling. The second harmonic generation (SHG) signal arising from the interaction of the two pulses is passed through a short-wave pass filter to block out any fundamental light that did not undergo SHG, and is focused into a single element HgCdT detector (Infrared Associates). This signal is integrated using a boxcar integrator, and collected using a digital-to-analog converter (Infrared Systems Development).
3. Results and discussion
Implementing pulse shaping experimentally requires two optical components. First, an apparatus is needed to spatially separate each frequency of the pulse. A zero-dispersion compressor consisting of gratings and lenses to separate and collimate each frequency of light is utilized for this purpose. The Ge-AOM is introduced into the ZDC line and fixed at the Fourier plane. The duration of the pulse is measured. In Fig. 2A , several intensity autocorrelations of the pulse are compared. First, the temporal duration of the pulse prior to entering the pulse shaper is 98 fs as noted in Fig. 2A. There is little change in the pulse duration after the ZDC line is constructed; the output pulse corresponds to what would be the zero-order diffraction of light with the Ge-AOM in place. With the Ge-AOM in place, the zero-order diffraction of the light is characterized after the shaper and is stretched in time to 650 fs due to the mid-IR pulse traveling through the 20mm thick crystal. This result is consistent with the work of Zanni and associates [25, 27]. Upon driving the constant frequency and amplitude acoustic wave through the Ge-AOM and directing the first-order diffraction output to the array detector, a frequency-time calibration is performed for the pulse shaper. In addition, a slit and the array detector are used to determine the presence of spatial dispersion and a spectrum of the pulse is inspected to ensure that none of the frequency components are clipped in the pulse shaper. If either of these problems exists, they are corrected prior to continuing with optimizing the pulse shaper. The pulse duration measured after the calibration is 3766 fs—this is almost 6 times larger than the pulse duration of the zero-order diffraction prior to activating the Ge-AOM. The autocorrelation trace is shown in Fig. 2A.
Fig. 2 Intensity autocorrelations of mid-IR pulses. Panel A compares the measured autocorrelations for mid-IR pulses traveling through the shaper device in a variety of configurations compared to mid-IR pulses not passing through the shaper. Only a combination of a Bragg angle corrected waveform and GVD/TOD corrections produce pulses with comparable pulse durations to the unmodified pulses. Panel B compared shaped pulses generated with and without the Bragg angle compensation. Both configurations were measured using GVD and TOD corrections optimized for the waveform type used. All autocorrelations are normalized.
There are steps to be taken to optimize the pulse shaper each of which aim to compensate for group velocity dispersion (GVD) and third-order dispersion (TOD) in the pulse as determined previously [25]. The second harmonic signal generated in a AgGaS2 crystal from the output pulses of the shaper is used for this optimization. Additional phase terms can be added to pulse shaping waveforms to compensate for GVD and TOD by expanding the phase as a function of frequency in a Taylor’s series expansion. Utilizing the AWG, a series of waveforms can be generated in order to scan the GVD and TOD terms, the SHG signal maxima is indicative of the appropriate GVD and TOD values to be used. The GVD and TOD terms determined for our pulse shaper using a constant amplitude waveform are 0.088 ps2 and −0.005 ps3 for GVD and TOD, respectively. Subsequently, the focal length from the second cylindrical mirror to the second grating is slightly adjusted using a translation stage under the second grating in order to further improve the SHG signal of the output of the shaper. The measured duration of this pulse is 255 fs and is shown in Fig. 2B. It is important to note that even though the FWHM of the pulse is significantly improved, long tails on the either side of the pulse still exist. The alignment of the shaper optics was performed several times producing the same result each time.
The optical bandwidth of our mid-IR pulses produced from the OPA is exceptional. The FWHM bandwidth of the pulse is routinely measured to be 900-1100 nm centered at either 5 μm or 6 μm, depending on the chemical system under investigation. This constitutes a change in the Bragg angle, ΔθB, equal to 0.44 degrees. For comparison, a visible pulse centered at 800 nm with a FWHM bandwidth of 100 nm, ΔθB is equal to 0.02 degrees. For practical consideration, an actuator on a mirror mount with 100 tpi (turns per inch) threads, 0.44 degrees constitutes greater than half a turn. Moreover, the wavevector mismatch that occurs with Bragg misalignment scales linearly; hence this angular dispersion will not improve at longer optical wavelengths, nor as optical bandwidths increase.
After implementing the new waveform developed above, a second GVD and TOD scan was performed. A new set of GVD and TOD values were determined to be 0.0441 ps2 and −0.005 ps3 for GVD and TOD, respectively. The autocorrelations of pulses produced from the shaper under these conditions are shown in Fig. 2A and Fig. 2B. The pulses are measured to be 125 fs in duration and the envelope returns to being nearly the same shape as the input mid-IR pulse. These pulse durations are similar to those previously reported after applying corrections for temporal dispersion [25]. From this data it is evident that the wavevector mismatch produced in the pulse shaper must be mitigated in order to efficiently shape broadband mid-IR pulses. Since the AOM produces both material dispersion from the Ge crystal and angular dispersion from the varying Bragg angle conditions, both must be accounted for in order to produce short pulses. With short pulses in hand, we moved on to generate pulse pairs required for 2D IR experiments. Autocorrelations of pulse pairs with several different time delays are shown in Fig. 3A . When an autocorrelation of a pulse pair is performed, three peaks are observed in the trace. There is one large peak present at the middle of the plot resulting from both pulse pairs being temporally overlapped, and there are two side peaks with half of the intensity resulting from one pulse from each pulse pair overlapping. The distance between the middle peak and a side peak is equal to the time delay between the two pulses. A 2D IR spectrum of W(CO)6 in hexane is presented in Fig. 3B. In addition to our active Bragg-angle compensating waveform in the experiment, phase cycling schemes developed by Zanni and associates were employed for transient absorption and scatter removal [20]. Thus, our new waveform does not hamper any previously developed capabilities, nor does it require the use of additional pulses produced by the regenerative amplifier.
Fig. 3 (A) Intensity autocorrelations of mid-IR pulse pairs generated using a Bragg angle corrected double pulse mask with pulse pair separations of 0.5 ps, 1 ps, 2 ps, and 3 ps. All autocorrelations are normalized time zero peak. (B) FTIR and 2D-IR spectrum of the carbonyl stretch in W(CO)6 in hexane using the active Bragg-angle compensating pulse pair mask and phase cycling to remove transient absorption and scatter.
4. Conclusions
The Ge-AOM is a spatial light modulator that operates in the Bragg regime. As such, the only diffraction order that will have significant light intensity is the first order diffraction line. Further, operating in the Bragg regime requires the incident and diffracted optical fields to meet the acoustic wave front at the Bragg angle. As optical bandwidth broadens to λo ± Δλ, angular dispersion is introduced because only λo is perfectly set to the Bragg angle. As Δλ increases, angular misalignment increases, thereby producing increasing amounts of angular dispersion in the pulse.
The effect of angular misalignment is small at visible wavelengths required by multidimensional electronic spectroscopy, because the fractional bandwidth in the AOM remains small [14]. However, at mid-IR wavelengths required for multidimensional IR spectroscopy the effect is significant because the fractional bandwidth in the AOM is ten-fold larger. The significance of the angular misalignment only grows as λo moves to longer wavelengths, for example far-IR, or the bandwidth, Δλ, increases. We have presented an approach to removing angular misalignment from a Bragg-regime pulse shaper by utilizing a waveform that actively compensates for the change in Bragg angle across the bandwidth of the optical pulse. The resulting acoustic wave in the Ge-AOM forces the acoustic wave front to a position that results in the proper Bragg angle for each optical frequency that is incident on the AOM. This approach to actively correcting the Bragg angle can be generalized to other optical frequencies and is especially promising for making pulse shaping technology compatible with broadband or continuum mid-IR pulsed light sources.
Acknowledgments
This work was supported by the ACS Petroleum Research Foundation (51228-DNI6) and through start-up funds provided by Colorado State University. J. M. Nite acknowledges the generous support of the Maciel Fellowship Fund.
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